In quantum mechanics, the Wigner–Weyl transform or Weyl–Wigner transform (after Hermann Weyl and Eugene Wigner) is the invertible mapping between functions...

Hermann Weyl in 1927, in a context related to representation theory in mathematics (see Weyl quantization). In effect, it is the Wigner–Weyl transform of the...

Wigner–Inonu contraction Wigner–Seitz cell Wigner–Seitz radius Wigner–Weyl transform Wigner–Wilkins spectrum Wigner's classification Wigner quasiprobability distribution...

arise in the phase space formulation of quantum mechanics through the Wigner transform of Heisenberg operators of canonical coordinates and momenta. These...

finally elucidated the consistent correspondence mechanism, the Wigner–Weyl transform, that underlies an alternate equivalent mathematical representation...

f_{2}]=\Phi [f_{1}]\Phi [f_{2}].\,} where Φ {\displaystyle \Phi } is the Wigner–Weyl transform. The star product is not commutative in general, but goes over to...

representation Wigner–Weyl transform CCR and CAR algebras (for bosons and fermions respectively) Segal–Bargmann space Moyal product Weyl algebra Stone's...

two-dimensional euclidean phase space) is given in the article on the Wigner–Weyl transform: two Gaussians compose with this ★-product according to a hyperbolic...

Wigner–Inonu contraction Wigner–Seitz cell Wigner–Seitz radius Wigner–Weyl transform Wigner–Wilkins spectrum Wigner's classification Wigner quasi-probability...

Mathematics Cotangent bundle Dynamic system Symplectic manifold Wigner–Weyl transform Physics Classical mechanics Hamiltonian mechanics Lagrangian mechanics...

Quantum chaos Quantum decoherence Quantum limit Semiclassical physics Wigner–Weyl transform WKB approximation Bohm, D. (1989). Quantum Theory. Dover Publications...

using the Fourier transform to a class of integrable functions larger than the polynomial functions), see Wigner–Weyl transform. Weyl algebras and Clifford...

and Wigner–Weyl transform). This more algebraic approach not only permits ultimately extending probability distributions in phase space to Wigner quasi-probability...

Donder–Weyl theory Hodge−Weyl decomposition Majorana–Weyl spinor Peter–Weyl theorem Schur–Weyl duality Weyl–Berry conjecture Weyl–Groenewold product Wigner–Weyl...

quantum observables, the most famous of these schemes being the Wigner–Weyl transform. It underlies Moyal’s dynamical equation, an equivalent formulation...

quantum field theory, the Weyl equation is a relativistic wave equation for describing massless spin-1/2 particles called Weyl fermions. The equation is...

Moyal product Noncommutative geometry Noncommutative standard model Wigner–Weyl transform It is possible to have a noncommuting time coordinate as in the...

transform Ray transfer matrix analysis de Bruijn, N. G. (1973). "A theory of generalized functions, with applications to Wigner distribution and Weyl...

Neumann theorem#Relation to the Fourier transform for details. Canonical commutation relations Wigner–Weyl transform Stone–von Neumann theorem Projective...

phase space as A(x, p) through the Wigner transform. Conversely, this operator may be recovered by the Weyl transform. The expectation value of the observable...

not semisimple and it does not satisfy Weyl's theorem on complete reducibility.) It was introduced by Eugene Wigner, to classify particles and fields in...

In relativistic quantum mechanics and quantum field theory, the Bargmann–Wigner equations describe free particles with non-zero mass and arbitrary spin...

Wigner's theorem, proved by Eugene Wigner in 1931, is a cornerstone of the mathematical formulation of quantum mechanics. The theorem specifies how physical...

fermion is transformed into the Newton–Wigner representation. The powerful machinery of the Foldy–Wouthuysen transform originally developed for the Dirac...

Royal Statistical Society B, 11, (1949), 150–210. Moyal bracket Wigner–Weyl transform Wigner quasiprobability distribution Gani, J. (1998). "Obituary: José...

was the first to achieve full understanding of the Wigner–Weyl transform as an invertible transform, rather than as an unsatisfactory quantization rule...

fields, but this was phenomenological. Weyl found a relativistic equation in terms of the Pauli matrices; the Weyl equation, for massless spin-1/2 fermions...

Hermann Weyl, but the Lorentz group has also received special attention due to its importance in physics. Notable contributors are physicist E. P. Wigner and...

the Wigner function by smearing with a Gaussian. This connection will be made more precise below, after we introduce the Segal–Bargmann transform. One...

In quantum mechanics, the Wigner's 3-j symbols, also called 3-jm symbols, are an alternative to Clebsch–Gordan coefficients for the purpose of adding angular...